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3 years ago

Which value for x would make the perimeter of this rectangle equal 48 inches

Mathematics

1 answer:

RSB [31]3 years ago

5 0

Answer:

L = 16; W=8: are the correct values.

Step-by-step explanation:

Start off with 2 math statements:

First, for the perimeter: 2W x 2L = 48

Then, for the area: W x L = 128

Next, we want to take the 2nd equation; then solve it for "W"

W x L = 128

Divide out both sides by "L", to get the "W" equals:

W = 128/L

Next, go back to the first equation. Where it indicates "W", put in the value of: 128/L in its place; to get:

2L + 2*(128/L) = 48; which gives us:

2L + 256/L = 48

Multiply everything by "L", to get:

2L2 + 256 = 48L

Next, divide out everything by 2, to get:

L2 + 128 = 24L

Next, move the 24L over to the left, to get:

L2 - 24L + 128 = 0

(L-16)* (L-8) = 0

L-16 = 0; L-8 = 0

Which gives us: L=16; L=8

Let's go with the L=16 first; back into the original equation:

f(16) = 2*16 + 2W = 48

32 + 2W = 48

-=32 -32

2W = 16

Divide out both sides by 2, to get:

W = 8

Next, test our values, by plugging them back into both original equations:

2*16 + 2*8 = 48

32 + 16 = 48 [Check]

L x W = 128

16 * 8 = 128

128 = 128 [Check]

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During one calendar year, a state trooper issued a total of 375 citations for warnings and speeding tickets. Of these, there wer

timama [110]

Answer:

169 Speeding Tickets, 206 Warnings.

Step-by-step explanation:

If there were 37 more warnings than tickets, then the first thing you want to do is remove that from the total by subtracting it: 375-37 = 338.

You then halve this to split them into tickets and warnings: 338/2 = 169.

Lastly, you add back the 37 more warnings, giving you 169 speeding tickets and 206 warnings.

6 0

3 years ago

A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 ft from the house, the

lord [1]

Answer:

a. -5 ft per sec

b. 59.5 ft² per sec

Step-by-step explanation:

a. Suppose l represents the ladder, x represents the height of the top of ladder from the base of house and y represents the distance of base of ladder from the base of house.

By the Pythagoras theorem,

$l^2 = x^2 + y^2------(1)$

Differentiating with respect to t ( time ),

$2l\frac{dl}{dt} = 2x \frac{dx}{dt}+2y\frac{dy}{dt}$

But, height of ladder, l = 13 ft = constant,

$\implies \frac{dl}{dt}=0$

$\implies 0= 2x \frac{dx}{dt}+2y\frac{dy}{dt}-----(2)$

We have,

y = 5, $\frac{dy}{dt}=12\text{ ft per sec}$ ,

Again by equation (1),

$13^2 = x^2 + 5^2\implies 169 = x^2 + 25\implies 169 - 25 = x^2\implies 144 = x^2\implies x = 12\text{ ft}$

From equation (2),

$0 = 2(12) \frac{dx}{dt} + 2(12)(5)$

$0= 24\frac{dx}{dt}+120$

$-120 =24\frac{dx}{dt}$

$\implies \frac{dx}{dt}=-\frac{120}{24}=-5\text{ ft per sec}$

Hence, the rate of change of the height of the top of the ladder is -5 ft per sec.

b. Now area of the triangle = 1/2 × base × height

$\implies A = \frac{1}{2}\times y\times x$

Differentiating with r. t. t,

$\frac{dA}{dt}=\frac{1}{2}(y\frac{dx}{dt}+x\frac{dy}{dt})$

$= \frac{1}{2}(5(-5) + 12(12))$

$=\frac{1}{2}(-25 + 144)$

$=\frac{119}{2}$

= 59.5 ft² per sec

Hence, area of the triangle is changing with the rate of 59.5 ft per sec.

7 0

4 years ago

What is fifteen lots of sixteen?

Brilliant_brown [7]

Answer:

240

Step-by-step explanation:

fifteen lots of sixteen = 15x16

15x16=240

4 0

2 years ago

Jayne is studying urban planning and finds that her town is decreasing in population by 3% each year. The population of her town

katen-ka-za [31]

This statement is in fact true

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3 years ago

Is there anyone who is expert in maths ?I’m in grade 9 can someone help me with maths pls tomorrow is my exam :(

sammy [17]

Answer:

Expert? Sorry, not me, but what sort of questions do you have?

Step-by-step explanation:

7 0

3 years ago